Answer:
3.725 x 10^6 is the scientific notation
Use the inverse of the coefficient matrix to solve the system of equations.
x+2y+3z = 11
2x+3y+4z = -10
−x−4y−8z = −66
Answer:
(x, y, z) = (-62, 50, -9)
Step-by-step explanation:
You want the solution to this system of equations using the inverse of the coefficient matrix.
x+2y+3z = 11
2x+3y+4z = -10
−x−4y−8z = −66
Inverse matrixThe inverse of the coefficient matrix is the transpose of the cofactor matrix, divided by the determinant. There are some shortcuts that can be used to make the computation easier. Easiest is letting a calculator find the matrix inverse. (See the first attachment.)
SolutionThe solution to the set of equations is the product of the inverse matrix and the constant vector on the right of the equal signs. That, too, can be found using a calculator. (See the second attachment.)
The solution is (x, y, z) = (-62, 50, -9).
Calculate the average rate of change of the given function f over the intervals [a, a + h] where h = 1, 0.1, 0.01, 0.001, and 0.0001. (Technology is recommended for the cases h = 0.01, 0.001, and 0.0001.) (Round your answers to seven decimal places.) f(x)=x^2/8; a = 1
The average rate of change of the given function f over the intervals-
f(x) = x²/8 ; x=a=1
the average rate of change of f(x) over the time interval [a, a + h] is
rc= [f(a +h) - f(a) ] / [(a +h)-a] = [(a +h)²/8 - a²/8] /h = 1/h [ (a²/8 +a*h/4+ h²/8) - a²/8]
= a /4+ h/8
then
rc= a/4+ h/8
for x=a=1 and h=1
rc= 1/4 + 1/8 = 0.375
for a=1 and h=0.1
rc= 1/4 + 0.1/8 = 0.2625
for a=1 and h=0.01
rc= 1 /4+ 0.01/8 = 0.25125
for a=1 and h=0.001
rc= 1/4 + 0.001/8 = 0.250125
for a=1 and h=0.0001
rc= 1 /4+ 0.0001/8 = 0.2500125
when h goes smaller , the average rate of change gets closer to the instantaneous rate of change of f(x) in x=a=1 (the derivative of f in a=1) , that is
f'(x) = x
then
f'(a) = a
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please help need asap
Answer: X = 21/6
Step-by-step explanation:
The angle is a 90 degree angle.
that means we know 21x+6=90
21x = 90-6
21x=84
x = 84/24
x = 21/6
x = 21/6
(URGENT) Lines a & m are parallel. Using the diagram below, what is the degree measure of angle 3?
Enter the numerical answer only. Example, if the answer is 12 degrees, only enter 12.
The value of angle 3 is 127 degrees.
How to find angles formed by parallel lines?Parallel lines are those lines that are equidistant from each other and never meet.
Parallel lines cut by a transversal, forms different angle relationship like alternate angles, corresponding angles, etc.
The line a and m are parallel lines.
The parallel lines are cut by a transversal y.
The angles formed are 1, 2, 3, 4, 5, 6, 7, 127 degrees etc.
This angles are related by alternate rule or corresponding rule.
Therefore,
∠3 is an alternate angle to 127 degrees.
Hence, alternate angles are congruent.
Therefore,
∠3 = 127 degrees.
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7x7=7X (5+____________)
=( __________ × 5) + (7 ×______ )
=______ + ______
=______
Find exact value of 6 trigonometric functions of angle 11pi/3
Answer:
sin 11pi/3 = - root3/2
cos 11pi/3 = 1/2
tan 11pi/3 = - root3
csc11pi/3 =-2root3/3
sec11pi/3= 2
cot11pi/3 = -root3/3
see image
Step-by-step explanation:
This is a question that you should use the Unit Circle to find the answers. Unit Circle looks like a horrible math nightmare pizza, but it is really a great big giant Answer Key. It has all the trig answers on it.
First, change 11pi/3 to an angle that IS on the Unit Circle. See image for three ways to change 11pi/3 to an equivalent (on the UnitCircle) angle 5pi/3.
Then, since the Unit circle is the Answer Key. Use the x and y given, in the form (x, y) to find all 6 trig values.
Memorize for this type of question:
sin = y (they both have that long i sound)
cos = x
tan = y/x
csc (flip over sin) = 1/y
sec = 1/x (flip cos)
cot = x/y (flip tan)
Also, to make things hairier, you have to know how to rationalize the denominator. This just means you canNOT leave a sqrt symbol on the bottom of a fraction.
And unfortunately, if you never learned how to manipulate a fraction over a fraction, you will have to do that too. Use Keep-Change-Flip. That makes it super do-able. See image.
A parachutist's rate during a free fall reaches 70 meters per second. What is this rate in feet per second? At this rate, how many feet will the parachutist fall during 2 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.
The rate of feet per second is 231 ft/sec and parachutists will fall 462 ft in 2 seconds.
What do we mean by speed?The definition of speed is The rate at which an object's position changes in any direction. Speed is defined as the ratio of distance traveled to time spent traveling. Because it has only one direction and no magnitude, speed is a scalar quantity.So, let's assume that y70m/s is the terminal velocity.
As 1 meter = 3.3 feetThen, 70 meters = 70 × 3.3 = 231 ft/secParachutist will fall at what rate in 2 seconds: 462 ft/secTherefore, the rate of feet per second is 231 ft/sec and parachutists will fall 462 ft in 2 seconds.
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A group of 25 students participated in a science competition. Their scores are below.
Score (points) 30-39 40-49 50-59 60-69 70-79
Number of Students
5
7
6
4
3
Would a dot plot or a histogram best represent the data presented here? Why?
O Histogram, because a large number of scores are reported as ranges
O Histogram, because a small number of scores are reported individually
O Dot plot, because a large number of scores are reported as ranges
O Dot plot, because a small number of scores are reported individually
The best graphical representation used to represent the score of 25 students is option A " Histogram, because a large number of scores are reported as ranges "
Histogram is the graphical representation of distribution of numerical data. The histogram look like a bar graph in appearance, but the frequency of numerical data using rectangles.
In histogram the range is the width of the rectangular bar along the x-axis. The range in the histogram is an approximate value.
In the given data, there are large number of scores are reported. So the given data will be represented in histogram. Therefore correct option is option A "Histogram, because a large number of scores are reported as ranges
Hence, the best graphical representation used to represent the score of 25 students is option A " Histogram, because a large number of scores are reported as ranges "
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2. Create a sequence to fit the given criteria. Describe your
sequence using figures, words, or numbers. Provide the first
four terms of the sequence. Explain how you know that it is
a sequence.
a. Create a sequence that begins with a positive integer, is
decreasing by multiplication, and is finite.
Need help quick please
A geometric sequence with first term 16 and common ratio 0.5, with 10 terms, satisfies the requirements for this problem, and the first four terms are:
16, 8, 4, 2.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
For this problem, we have that:
Sequence begins with a positive integer, hence the first term is 16. (chosen value, any positive integer suffices).The sequence is decreasing by multiplication, hence q > 0 and q < 1, q = 0.5 is a possible value and the sequence is geometric.A finite number of terms, we chose 10.Each term is the previous term multiplied by 0.5, hence the first four terms are:
16, 8, 4, 2.
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the total of the square of a number n and the difference between seventeen and the square of the number
Answer:
Step-by-step explanation:
n²+(17-n²)=n²+17-n²=17
Answer: n²+(17-n²)=n²+17-n²=17
Step-by-step explanation:
a(1)=−2 a(n)=a(n−1)−5
Answer:
What do I solve for?
Step-by-step explanation:
Which of the following shows the correct solution steps and solution to
7x-4--18?
O A.
7x-4 =-18
7x-4-4 = -18-4
7x = −14
7x
-14
7
7
=
-
x = -2
The solution for the equation 7x-4 = -18 is x = -2
The equation given is, 7x - 4 = -18.
We will try to solve this equation using elimination method in the following steps.
7x-4= -18
⇒ 7x-4+4 = -18+4
⇒7x = -14
⇒7x/7 = -14/7
⇒x = -2 is the solution for the given equation.
In the first step, we added 4 on both sides to eliminate -4 on the left side.
In the next step, we divided the both sides by 7 to eliminate the 7 on the left side. Finally, we got the solution as x = -2.
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can someone help me with this
We get that the value of (f + g)(x) is 11 x - 1.
Function: a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
We are given the two functions:
f(x) = 4 x + 3
g(x) = 7 x - 4
We need to find:
(f + g)(x)
We know that this is equal to
= f(x) +g(x)
Substituting the values, we get that:
= 4 x + 3 + 7x - 4
Combining the like terms, we get that:
= 11 x - 1
Therefore, we get that the value of (f + g)(x) is 11 x - 1.
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The diagram shows three vertical poles X, Y and Z. Calculate the distance between Pole X Pole Z.
Using the Pythagorean Theorem, the distance between Pole X and Pole Z is of 15.3 m.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
The first part of the distance is the hypotenuse of a right triangle of sides 0.5 and 2.5, tracing a right triangle at the top of pole X and tracing it to segment Y, hence:
df² = 0.5² + 2.5²
df = sqrt(0.5² + 2.5²)
df = 2.55m.
For the second part, we apply equivalent triangles, as we can also trace a right triangle at the top of segment Y to segment Z, hence:
0.5/2.5 = df/ds
1/5 = 2.55/ds
ds = 2.55 x 5 = 12.75m
Then the total distance is:
2.55 + 12.75 = 15.3 m.
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Which of the following choices shows the standard form of the equation below?
y= -3/2x +5
A) 3x+2y=10
B) 3x-2y=10
C) -2y-3x=26
D) 3x+2y=26
Answer:
A
Step-by-step explanation:
y=3/2x+5
2(y+3/2x)=5(2)
2y+3x=10
Simplify and determine the coefficient of (- 2/3 x)(3y)(-2x).
4
-4
1/3
1
Answer:
Welcome to Gboard clipboard, any text you copy will be saved here. Welcome to Gboard clipboard, any text you copy will be saved here.
Step-by-step explanation:
A
Juliana is taking out an $8,700, 3-year loan with an APR of 2.31%. What will be the monthly payment for this loan? Round to the nearest cent.
Answer: $250.37
Step-by-step explanation: no clue teacher told me because she doesn't know
The right triangle drawn on the road sign is 10 inches high. If the base of the right triangle is 5 inches, what is the
area of the right triangle formed in the sign?
O 48 sq.in.
O 64 sq.in.
O 25 sq.in.
O 36 sq.in.
Answer:
25 sq.in.
The area formula for the triangle is 1/2 b•h
1/2 divided by 5 is 2.5
2.5 x 10 is 25.
Step-by-step explanation:
What is the coefficient of the third term in this expression?
8-3n+ 10m + 4k
PLS HELP IMMA DIE
Jafari and adana are giving their dog a bath. The label on the shampoo bottle recommends a ratio of 1/6 of shampoo to water. what percent of the bath needs to be shampoo?
The percent of the bath needs to be shampoo will be 16.67%.
How to calculate the percentage?From the information, Jafari and adana are giving their dog a bath and the label on the shampoo bottle recommends a ratio of 1/6 of shampoo to water
The percent of the bath needs to be shampoo will be:
= 1/6 × 100
= 16.67%
Therefore, the percent of the bath needs to be shampoo will be 16.67%.
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Maysa made an error in her work on the following problem. 3 .5 − 2 . 46 = 1 . 16 Describe Maysa's error. Explain how you would use a model or place-value concepts to help Maysa build understanding. Give the correct answer in your explanation.
The error in the subtraction process is that 0.1 is not added to the 0 in the hundredth place of the term 3.5, so as to enable 0.06 to be subtracted from it.
The correct equation is as follows;
3.5 - 2.46 = 1.04Which method can be used to find the correct value to the equation?The given equation that has an error is presented as follows;
3.5 - 2.46 = 1.16
The description of the error in the above equation is that during subtraction, the 0.06 value on the right of the subtraction mark is not subtracted from the zero to the right of .5, and carried down.
The correct process for the subtraction is presented as follows;
3.5¹0
- 2.46
1.04
Therefore;
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SOLVE PROBLEMS WITH RATIOS AND PROPORTIONS
. A recipe uses a 2:5 ratio of baking soda to brown sugar Write an equation and find the missing quantity for
each situation.
a. How much brown sugar do you need if you want to use 6 tablespoons of baking soda?
b. How much baking soda do you need if you want to use 20 teaspoons of brown sugar?
c. How much brown sugar do you need if you want to use 4 cups of baking soda?
d. How much baking soda do you need if you want to use 60 grams of brown sugar?
Using proportions, it is found that:
a) You need 15 tablespoons of brown sugar.
b) You need 8 tablespoons of baking soda.
c) You need 10 cups of brown sugar.
d) You need 24 cups of baking soda.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for ratio problems.
For this problem, the recipe uses a 2:5 ratio of baking soda to brown sugar, hence:
2/7 of the recipe is of soda.5/7 of the recipe is of sugar.The amount of sugar is 5/2 of the amount of soda.The amount of soda is 2/5 of the amount of sugar.Hence, for item a, the amount is:
5/2 x 6 = 30/2 = 15.
You need 15 tablespoons of brown sugar.
For item b, the amount is:
2/5 x 20 = 40/5 = 8.
You need 8 tablespoons of baking soda.
For item c, the amount is:
5/2 x 4 = 20/2 = 10.
You need 10 cups of brown sugar.
For item d, the amount is:
2/5 x 60 = 120/5 = 24.
You need 24 cups of baking soda.
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Is 21.337 greater or less than 21.31
Answer: greater than
Step-by-step explanation:because 21.337 [tex]\leq[/tex] 21.310 or 21.31Answer:
Yes, because 21.337 rounded down is 21.34, and that is larger than 21.31
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)
suppose there are only two weather states: sunny and raining. If
today is sunny, the probability of raining for tomorrow is 0.6. If today is raining, the
probability of sunny for tomorrow is 0.7. Based on climatic records, during a year of 365
2
days, the number of sunny days is 265 days on average, and the remaining days are raining.
Please do the following
(1) What is the probability of sunny for tomorrow given today is sunny?
(2) What is the probability of raining for tomorrow given today is raining?
(3) Given today is sunny, what is the probability that yesterday is sunny as well?
Imagine there are only two possible weather conditions: sunny and rainy. If it's sunny today, there is a 0.6 percent probability it will rain tomorrow. If it rains today, there is a 0.7 percent probability that it will be sunny tomorrow. Based on climatic records, during a year of 365 2 days, the number of sunny days is 265 days on average, and the remaining days are raining.
Please do the following
(1) Given that today is sunny, what is the probability that tomorrow will be sunny?
(2) Given that it is raining today, what is the probability that it will rain tomorrow?
1. The probability of sunny for tomorrow given today is sunny is 0.4.
2. the probability of raining for tomorrow given today is raining is 0.3
Given that
If it's sunny today, there is a 0.6 percent probability it will rain tomorrow.
If it rains today, there is a 0.7 percent probability that it will be sunny tomorrow.
A year of 365 days, the number of sunny days is 265 days on average, and the remaining days are raining that are 100.
1. The probability of sunny for tomorrow given today is sunny is
1-0.6=0.4
2. the probability of raining for tomorrow given today is raining is
1-0.7=0.3
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South Beach Middle School has 1,272 total students. The students are
Divided into equal classes of 24 students each. How many classes are
There in all?
There are 53 classes in South Beach middle school
How to calculate the number of classes in the school ?South beach middle school has 1,272 students
The students are divided into equal classes of 24 students each
Therefore the number of classes can be calculated by dividing the total population of the students in the school by 24
= 1272/24
= 58
Hence there are 58 classes in the school
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2<3x-1 ≤ 5 solution to compound inequality
The solution of the inequality is 1<x<2.
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations.
According to the given statement;
2 < 3x - 1 < 5
or, 2 + 1 < 3x - 1 + 1 < 5 + 1
or, 3 < 3x < 6
Divide the whole by 3, we get
or, 3/3 < (3/3)x < 6/3
or, 1 < x < 2
hence, the solution of the inequality is 1<x<2.
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Express each decimal as a fraction -0.4
Answer:
It will be. - 4/10 only that
Determine if the statement is true or false. If it is false, explain what must be changed in the statement to make it true. If it is true, explain why you believe it to be true.
The common difference for the geometric sequence given by 1, -1, -3, -5, -7… is 2.
The statement is false and the changes to make the statement true are:
Change the sequence type to arithmetic sequenceChange the common difference to -2How to determine if the statement is true or false?The statement is given as:
The common difference for the geometric sequence given by 1, -1, -3, -5, -7… is 2.
The above statement is false because of the following reasons:
The sequence is an arithmetic sequence (not a geometric sequence)The common difference for the sequence is -2 not 2 i.e.. -1 - 1 = -2Hence, the statement is false and the changes to make the statement true are:
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given g(x) = -x - 4, find g(-2)
Answer: -2
Step-by-step explanation:
[tex]g(x) = g(-2) = -(-2)-4=2-4=-2[/tex]
Using long division what is the quotient of this expression
3x^4-2x^3-x-4
———————-
X^2+2
3x² - 2x -6 is quotient in polynomial after long division .
What in mathematics is a polynomial?
Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video.A polynomial is a mathematical expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. It is made up of indeterminates (also known as variables) and coefficients. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x.[tex]\frac{3x^{4} - 2x^{3} - x - 4 }{x^{2} + 2}[/tex]
after long division we get quotient - 3x² - 2x -6 .
Divide using long division: standard [tex]3x^{2} + \frac{3x + 8 }{x^{2} + 2} - 2x - 6[/tex]
quotient - 3x² - 2x -6
remainder - 3x + 8
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Answer:
see image
Step-by-step explanation:
Plato/Edmentum